This report is a review on aspects of constitutive modelling of high strength steels. Aspects that have been presented are basic crystallography of steel, martensite transformation, thermodynamics and plasticity from a phenomenological point of view. The phenomenon called mechanical twinning is reviewed and the properties of a new material type called TWIP-steel have been briefly presented. Focus has been given on phenomenological models and methods, but an overview over multiscale methods has also been given.

<p>This work deals with the problem of estimating the intrinsic dimension of noisy, high-dimensional point clouds. A general class of sets which are locally well-approximated by <italic>k</italic> dimensional planes but which are embedded in a <italic>D</italic>>><italic>k</italic> dimensional Euclidean space are considered. Assuming one has samples from such a set, possibly corrupted by high-dimensional noise, if the data is linear the dimension can be recovered using PCA. However, when the data is non-linear, PCA fails, overestimating the intrinsic dimension. A multiscale version of PCA is thus introduced which is robust to small sample size, noise, and non-linearities in the data.</p> / Dissertation

One of the important factors to be considered in designing an engineering system is uncertainty, which emanates from natural randomness, limited data, or limited knowledge of systems. In this study, a robust design methodology is established in order to design multifunctional materials, employing multi-time and length scale analyses. The Robust Concept Exploration Method with Error Margin Index (RCEM-EMI) is proposed for design incorporating non-deterministic system behavior. The Inductive Design Exploration Method (IDEM) is proposed to facilitate distributed, robust decision-making under propagated uncertainty in a series of multiscale analyses or simulations. These methods are verified in the context of Design of Multifunctional Energetic Structural Materials (MESM). The MESM is being developed to replace the large amount of steel reinforcement in a missile penetrator for light weight, high energy release, and sound structural integrity. In this example, the methods facilitate following state-of-the-art design capabilities, robust MESM design under (a) random microstructure changes and (b) propagated uncertainty in a multiscale analysis chain. The methods are designed to facilitate effective and efficient materials design; however, they are generalized to be applicable to any complex engineering systems design that incorporates computationally intensive simulations or expensive experiments, non-deterministic models, accumulated uncertainty in multidisciplinary analyses, and distributed, collaborative decision-making.

Polymer nanocomposites refer to a broad range of composite materials with polymer acting as the matrix and any material which has at least one dimension in the order of 1 ~ 100 nanometer acting as the filler. Due to unprecedented improvement observed in properties of the nanocomposites, research interest in this area has grown exponentially in recent years. In designing better nano-composites for advanced technological applications some of the major challenges are: understanding the structure-property relationships, interaction and integrity of the two components at the interface, the role of nanofillers in enhancing the properties of the resulting material. In our work, we have utilized first principle calculations, atomistic simulations, coarse-grained modeling and constitutive equations to develop structureproperty relationships for an amorphous aromatic piezoelectric polyimide substituted with nitrile dipole, carbon nanotubes and resulting nanocomposites. We have studied in detail structure-property relationships for carbon nanotubes and (? ?CN)APB/ODPA polyimide. We have developed chemically sound coarse-grained model based on atomic level simulations of the piezoelectric polyimide to address the larger length and time scale phenomena. The challenge of coarse grain model for these polymers is to reproduce electrical properties in addition to the structure and energetics; our model is the first to successfully achieve this goal. We have compared and analyzed atomistic scale simulation results on the nanocomposite with those predicted from micromechanics analysis. Notably, we have investigated the time dependent response of these highly complex polymers, to our best knowledge this is the first of its kind. In particular we have studied the thermal, mechanical and dielectric properties of the polyimide, nanotube and their nanocomposites through multi-scale modeling technique. We expect the results obtained and understanding gained through modeling and simulations may be used in guiding development of new nanocomposites for various advanced future applications. In conclusion we have developed a computational paradigm to rationally develop next generation nano-materials.

In this dissertation we discuss some upscaling methods for flow and transport in heterogeneous reservoirs. We studied realization-based multi-phase flow and transport upscaling and ensemble-level flow upscaling. Multi-phase upscaling is more accurate than single-phase upscaling and is often required for high level of coarsening. In multi-phase upscaling, the upscaled transport parameters are time-dependent functions and are challenging to compute. Due to the hyperbolic feature of the saturation equation, the nonlocal effects evolve in both space and time. Standard local two-phase upscaling gives significantly biased results with reference to fine-scale solutions. In this work, we proposed two types of multi-phase upscaling methods, TOF (time-offlight)- based two-phase upscaling and local-global two-phase upscaling. These two methods incorporate global flow information into local two-phase upscaling calculations. A linear function of time and time-of-flight and a global coarse-scale two-phase solution (time-dependent) are used respectively in these two approaches. The local boundary condition therefore captures the global flow effects both spatially and temporally. These two methods are applied to permeability distributions with various correlation lengths. Numerical results show that they consistently improve existing two-phase upscaling methods and provide accurate coarse-scale solutions for both flow and transport. We also studied ensemble level flow upscaling. Ensemble level upscaling is up scaling for multiple geological realizations and often required for uncertainty quantification. Solving the flow problem for all the realizations is time-consuming. In recent years, some stochastic procedures are combined with upscaling methods to efficiently compute the upscaled coefficients for a large set of realization. We proposed a fast perturbation approach in the ensemble level upscaling. By Karhunen-Lo`eve expansion (KLE), we proposed a correction scheme to fast compute the upscaled permeability for each realization. Then the sparse grid collocation and adaptive clustering are coupled with the correction scheme. When we solve the local problem, the solution can be represented by a product of Green's function and source term. Using collocation and clusering technique, one can avoid the computation of Green's function for all the realizations. We compute Green's function at the interpolation nodes, then for any realization, the Green's function can be obtained by interpolation. The above techniques allow us to compute the upscaled permeability rapidly for all realizations in stochastic space.

In order to create informed predictive models that capture artery dependent responses during atherosclerosis progression and the long term response to hypertension, one needs to know the structural, biochemical and mechanical properties as a function of time in these diseased states. In the case of hypertension more is known about the mechanical changes; while, less is known about the structural changes over time. For atherosclerotic plaques, more is known about the structure and less about the mechanical properties. We established a congruent multi-scale model to predict the adapted salient arterial geometry, structure and biochemical response to an increase in pressure. Geometrical and structural responses to hypertension were then quantified in a hypertensive animal model. Eventually this type of model may be used to predict mechanical changes in complex disease such as atherosclerosis. Thus for future verification and implementation we experimentally tested atherosclerotic plaques and quantified composition, structure and mechanical properties. Using the theoretical models we can now predict arterial changes in biochemical concentrations as well as salient features such as geometry, mass of elastin, smooth muscle, and collagen, and circumferential stress, in response to hemodynamic loads. Using an aortic coarctation model of hypertension, we found structural arterial responses differ in the aorta, coronary and cerebral arteries. Effects of elevated pressure manifest first in the central arteries and later in distal muscular arteries. In the aorta, there is a loss and then increase of cytoskeleton actin fibers, production of fibrillar collagen and elastin, hyperplasia or hypertrophy with nuclear polypoid, and recruitment of hemopoeitic progenitor cells and monocytes. In the muscular coronary, we see similar changes albeit it appears actin fibers are recruited and collagen production is only increased slightly in order to maintain constant the overall ratio of ~55 percent. In the muscular cerebral artery, despite a temporary loss in actin fibers there is little structural change. Contrary to hypertensive arteries, characterizing regional stiffness in atherosclerotic plaques has not been done before. Therefore, experimental testing on atherosclerotic plaques of Apolipoprotein E Knockout mice was performed and revealed nearly homogenously lipidic plaques with a median axial compressive stiffness value of 1.5 kPa.

In this dissertation we develop and analyze numerical method to solve general elliptic boundary value problems with many scales. The numerical method presented is intended to capture the small scales e&#64256;ect on the large scale solution without resolving the small scale details, which is done through the construction of a multiscale map. The multiscale method is more e&#64256;ective when the coarse element size is larger than the small scale length. To guarantee a numerical conservation, a &#64257;nite volume element method is used to construct the global problem. Analysis of the multiscale method is separately done for cases of linear and nonlinear coe&#64259;cients. For linear coe&#64259;cients, the multiscale &#64257;nite volume element method is viewed as a perturbation of multiscale &#64257;nite element method. The analysis uses substantially the existing &#64257;nite element results and techniques. The multiscale method for nonlinear coe&#64259;cients will be analyzed in the &#64257;nite element sense. A class of correctors corresponding to the multiscale method will be discussed. In turn, the analysis will rely on approximation properties of this correctors. Several numerical experiments verifying the theoretical results will be given. Finally we will present several applications of the multiscale method in the &#64258;ow in porous media. Problems that we will consider are multiphase immiscible &#64258;ow, multicomponent miscible &#64258;ow, and soil in&#64257;ltration in saturated/unsaturated &#64258;ow.

This dissertation is the first attempt to demonstrate the use of magnetic-levitation (maglev) positioners for commercial applications requiring nanopositioning. The key objectives of this research were to devise the control strategies and motion planning to overcome the inherent technical challenges of the maglev systems, and test them on the developed maglev systems to demonstrate their capabilities as the next-generation nanopositioners. Two maglev positioners based on novel actuation schemes and capable of generating all the six-axis motions with a single levitated platen were used in this research. These light-weight single-moving platens have very simple and compact structures, which give them an edge over most of the prevailing nanopositioning technologies and allow them to be used as a cluster tool for a variety of applications. The six-axis motion is generated using minimum number of actuators and sensors. The two positioners operate with a repeatable position resolution of better than 3 nm at the control bandwidth of 110 Hz. In particular, the Y-stage has extended travel range of 5 mm × 5 mm. They can carry a payload of as much as 0.3 kg and retain the regulated position under abruptly and continuously varying load conditions. This research comprised analytical design and development, followed by experimental verification and validation. Preliminary analysis and testing included open-loop stabilization and rigorous set-point change and load-change testing to demonstrate the precision-positioning and load-carrying capabilities of the maglev positioners. Decentralized single-input-single-output (SISO) proportional-integral-derivative (PID) control was designed for this analysis. The effect of actuator nonlinearities were reduced through actuator characterization and nonlinear feedback linearization to allow consistent performance over the large travel range. Closed-loop system identification and order-reduction algorithm were developed in order to analyze and model the plant behavior accurately, and to reduce the effect of unmodeled plant dynamics and inaccuracies in the assembly. Coupling among the axes and subsequent undesired motions and crosstalk of disturbances was reduced by employing multivariable optimal linear-quadratic regulator (LQR). Finally, application-specific nanoscale path planning strategies and multiscale control were devised to meet the specified conflicting time-domain performance specifications. All the developed methodologies and algorithms were implemented, individually as well as collectively, for experimental verification. Some of these applications included nanoscale lithography, patterning, fabrication, manipulation, and scanning. With the developed control strategies and motion planning techniques, the two maglev positioners are ready to be used for the targeted applications.

All materials are heterogeneous at various scales of observation. The influence of material heterogeneity on nonuniform response and microstructure evolution can have profound impact on continuum thermomechanical response at macroscopic "engineering" scales. In many cases, it is necessary to treat this behavior as a multiscale process. This research developed a hierarchical multiscale approach for modeling microstructure evolution. A theoretical framework for the hierarchical homogenization of inelastic response of heterogeneous materials was developed with a special focus on scale invariance principles needed to assure physical consistency across scales. Within this multiscale framework, the second gradient is used as a nonlocal kinematic link between the response of a material point at the coarse scale and the response of a neighborhood of material points at the fine scale. Kinematic consistency between two scales results in specific requirements for constraints on the fluctuation field. A multiscale internal state variable (ISV) constitutive theory is developed that is couched in the coarse scale intermediate configuration and from which an important new concept in scale transitions emerges, namely scale invariance of dissipation. At the fine scale, the material is treated using finite element models of statistical volume elements of microstructure. The coarse scale is treated using a mixed-field finite element approach. The coarse scale constitutive equations are implemented in a finite deformation hyperelastic inelastic integration scheme developed for second gradient constitutive models. An example problem based on an idealized porous microstructure is presented to illustrate the approach and highlight its predictive utility. This example and a few variations are explored to address the boundary-value-problem dependent nature of length scale parameters employed in nonlocal continuum theories. Finally, strategies for developing meaningful kinematic ISVs, free energy functions, and the associated evolution kinetics are presented. These strategies are centered on the goal of accurately representing the energy stored and dissipated during irreversible processes.

Ni-base superalloys are widely used in hot sections of gas turbine engines due to the high resistance to fatigue and creep at elevated temperatures. Due to the demands for improved performance and efficiency in applications of the superalloys, new and improved higher temperature alloy systems are being developed. Constitutive relations for these materials need to be formulated accordingly to predict behavior of cracks at notches in components under cyclic loading with peak dwell periods representative of gas turbine engine disk materials. Since properties are affected by microstructure at various length scales ranging from 10 nm tertiary γ' precipitates to 5-30 μm grains, hierarchical multiscale modeling is essential to address behavior at the component level. The goal of this work is to develop a framework for hierarchical multiscale modeling network that features linkage of several fine scale models to incorporate relevant microstructure attributes into the framework to improve the predictability of the constitutive model. This hierarchy of models is being developed in a collaborative research program with the Ohio State University. The fine scale models include the phase field model which addresses dislocation dissociation in the γ matrix and γ' precipitate phases, and the critical stresses from the model are used as inputs to a grain scale crystal plasticity model in a bottom-up fashion. The crystal plasticity model incorporates microstructure attributes by homogenization. A major task of the present work is to link the crystal plasticity model, informed by the phase field model, to the macroscale model and calibrate models in a top-down fashion to experimental data for a range of microstructures of the improved alloy system by implementing a hierarchical optimization scheme with a parameter clustering strategy. Another key part of the strategy to be developed in this thesis is the incorporation of polycrystal plasticity simulations to model a large range of virtual microstructures that have not been experimentally realized (processed), which append the experimentally available microstructures. Simulations of cyclic responses with dwell periods for this range of virtual (and limited experimental) polycrystalline microstructures will be used to (i) provide additional data to optimize parameter fitting for a microstructure-insensitive macroscopic internal state variable (ISV) model with thermal recovery and rate dependence relevant to the temperatures of interest, and (ii) provide input to train an artificial neural network that will associate the macroscopic ISV model parameters with microstructure attributes for this material. Such microstructure sensitive macroscopic models can then be employed in component level finite element studies to model cyclic behavior with dwell times at smooth and cracked notched specimens.